Well there are different area's where the concept of form factor is used. Eg : electronics, PC-engineering and high energy physics. In the latter, the form factor is defined as the Fourier transforms of charge and current distributions. Basically, one could look at the form factor as the strength of an interaction (electrical and magnetic) in the Fourier base. This concept is widely used in effective field theories in which the basic degrees of freedom (like particles for example) are NOT elementary.

Thank you, Malon. I found this in the cross section of e-e+ to vector meson. Is there another meaning of form factor in high energy physics.

Well, i guess there are other ways to look at it but the basic idea will be the "link to strength of interaction". I know there is also a topological explanation where you can plot the form factor as a surface. The deformation of that surface during an interaction gives an idea about what is going on and how strong that interaction is. In QHD (quantum hadro dynamics), this is used very often.

For invariant amplitude and invariant mass amplitude, I think they are the same. We calculate them on the way to find the cross section. So, how does it relate to mass if both are the same? I am a bit confused.

For invariant amplitude and invariant mass amplitude, I think they are the same. We calculate them on the way to find the cross section. So, how does it relate to mass if both are the same? I am a bit confused.

Mass ??? Keep in mind that mass is not the coupling constant of electromagnetic or (in general) weak interactions. Again, read the definition in the paper, the key notion is the "squared four momentum Q² dependency" .

I'm sorry that the topic had changed. I didn't ask you about the form factor but I asked you about the invariant mass amplitude or invariant amplitude that we can meet them on the way to find the cross-section,
for example, the cross section of e-e+ annihilation and the cross section of mu-decay.